Mathematics
posted by Joe .
OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid, the volume of the pyramid, and the total surface area of the pyramid by first drawing the net of the pyramid.

sqrt ( 15 ^ 2  12 ^ 2 ) = sqrt ( 225 144 ) = sqrt ( 81 ) = 9 cm

Draw one of the side triangles, and consider its altitude from the base of 12, call that x
x^2 + 6^2 = 15^2
x^2 = 19
x =√189
so the surface area = the base + 4triangles
= 144 + 4(1/2)(12)(√189) = ....
for the volume , we need the height of the pyramid,
call it h
h^2 + 6^2 = (√189)^2
h^2 = 153
h = √153
volume = (1/3)(base)(height)
= (1/3)(144)(√153
= 48√153 
A right pyramid has a square base 6cm by 6cm and each face has a slant height of 5 cm. Calculate the height of pyramid